Solve for $x$ and $y$ using elimination. ${x-3y = -3}$ ${-x+4y = 7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x-3y = -3}\thinspace$ to find $x$ ${x - 3}{(4)}{= -3}$ $x-12 = -3$ $x-12{+12} = -3{+12}$ ${x = 9}$ You can also plug ${y = 4}$ into $\thinspace {-x+4y = 7}\thinspace$ and get the same answer for $x$ : ${-x + 4}{(4)}{= 7}$ ${x = 9}$